The Optimization Solution Algorithm And Parameters Analysis Of One Portfolio Model

Based on the Markowitz M-V model in this article,the expectation is considered as one condition, the linear combination of the variance and skewness is regarded as objective function, so the non-linear programming is formed. The objective function is approached by the piecewise linear function. We substitute the expectation for sample mean. So the non-linear programming is transformed into linear programming which we try to analyze to get the local analytic solution. We can solve it with the simplex algorithm to get the minimum and realize the purpose of getting the portfolio optimization. Then we graphs diagrams with numerical groups solved and discuss the correlation between objective function values and parameters. So we obtain the simple conclusions.First we discuss how to transform in detail. There are two cases during transforming. When it is s = xr ? Exr≤0, the portfolio return rate is lower than the investor expected rate of portfolio return, this is one. When it is s = xr ? Exr≥0,the rate of portfolio return is higher than the investor expected rate of portfolio return. This is another. Because of Markowitz's theory of portfolio selection the variance isn't equal zero under these two cases and there are both risk. Then we do with portfolio selection model with transaction cost. We will discuss two kinds of way to charge transaction cost which are used usually in market. It is discussed in detail to charge constant cost per change in the proportion of every asset . We use new variables to deal with non-smooth programming problem including absolute values. After obtaining linear programming problem we try to research on it to get local analytic solution.A numerical example is given to illustrate the algorithm for presented linear programming problems and how to program. First we calculate the specific linear programming problems under two cases and program the calculating method. Then we discuss how to solve and program the specific problem with transaction cost. We figures diagrams with sixteen numerical groups in the two- and three-dimension coordinate. So...